\subsection{Gaussian One}
The first gaussian had a covariance of the following: $\Sigma = \begin{smallmatrix} 1&0\\ 0 & 3 \end{smallmatrix}$, and a mean of $\mu = \begin{smallmatrix}0 & 0\end{smallmatrix}$.

\begin{enumerate}
\item See figure \ref{fig:oneContour}. Octave would not print the legend correctly to file\footnote{This is a known bug}. The values for $x_2$ in the last subplot
are $x2 = $\color{blue}−3, \color{red}−2, \color{green}-1, \color{black} 0, \color{magenta} 1, \color{cyan} 2,\color{yellow}3\color{black}.

\begin{figure}[h]
	\centering
	\includegraphics[width=\textwidth]{resources09/gaussianContourOne}
    \label{fig:oneContour}
    \caption{The gaussian contour plot, the marginal distribution over $x_1$ and the distribution over $x_1$ for different values of $x_2$.}
\end{figure}


\item
The marginal distribution over $x_1$ is: $p(x_1) = N(x; 0, 1)$.

\item See figure \ref{fig:oneContour} once more. The figure shows that the 
values sign of a value for $x_2$ is irrelevant.

\end{enumerate}


\subsection{Gaussian Two}
The second gaussian had a covariance of the following: $\Sigma = \begin{smallmatrix} 1&.7\\ .7 & 1 \end{smallmatrix}$. The mean remained the same. 

\begin{enumerate}
\item We used \texttt{mesh} instead of \texttt{plot3d}, because we found not function named \texttt{plot3d}. See figure \ref{fig:twoContour} for the result.

\begin{figure}
	\centering
	\includegraphics[width=\textwidth]{resources09/gaussian3d}
    \label{fig:twoContour}
    \caption{The 3d gaussian plot and the distribution over $x_1$ for different values of $x_2$.}
\end{figure}

\item
This is the same as for gaussian one: $p(x_1) = N(x; 0, 1)$.

\item Once more, the values for $x_2$ 
are $x2 = $\color{blue}−3, \color{red}−2, \color{green}-1, \color{black} 0, \color{magenta} 1, \color{cyan} 2,\color{yellow}3\color{black}.

\end{enumerate}
